Math. 350-01, Spring, 2000, Second Examination

Problem 2 Answers

sol1  =  
      DSolve[{v'[t]  ==  -32  - k*v[t], v[0] == 0}, v[t], t]

sol2  =  
      DSolve[{v'[t]  ==  -32 + K*v[t]^2,  v[0] == 0},  v[t], t]

v1[t_]  =  
      Simplify[v[t]  /.  First[sol1]  /.  {k -> 0.178}]

v2[t_]  =  
      Simplify[v[t]  /.  First[sol2]  /.  {K  ->  0.000988}]

Plot[{v1[t]}, {t, 0, 30}, PlotRange  ->  {-180, 0}]

Plot[{v2[t]}, {t, 0, 30}, PlotRange  ->  {-180, 0}]

Plot[{v1[t], v2[t]}, {t, 0, 30}, PlotRange  ->  {-180, 0}]

The speed corresponding to equation (2) increases more rapidly initially, then levels off faster.  It is hard to tell which equation models the actual fall better without observing someone falling and taking time and altitude measurements.  However, v1 probably is a better approximation for small t and v2 is probably a better approximation for larger t, as turbulence sets in mainly for the larger velocities.